A mixed-effects model is represented as a
merPredD object and a response
module of a class that inherits from class
lmResp. A model with a
lmerResp response has class lmerMod; a
glmResp response has class glmerMod; and a
nlsResp response has class nlmerMod.
Usage
## S3 method for class 'merMod'
anova(object, ..., refit = TRUE, model.names=NULL)
## S3 method for class 'merMod'
coef(object, ...)
## S3 method for class 'merMod'
deviance(object, REML = NULL, ...)
REMLcrit(object)
## S3 method for class 'merMod'
extractAIC(fit, scale = 0, k = 2, ...)
## S3 method for class 'merMod'
family(object, ...)
## S3 method for class 'merMod'
formula(x, fixed.only = FALSE, random.only = FALSE, ...)
## S3 method for class 'merMod'
fitted(object, ...)
## S3 method for class 'merMod'
logLik(object, REML = NULL, ...)
## S3 method for class 'merMod'
nobs(object, ...)
## S3 method for class 'merMod'
ngrps(object, ...)
## S3 method for class 'merMod'
terms(x, fixed.only = TRUE, random.only = FALSE, ...)
## S3 method for class 'merMod'
vcov(object, correlation = TRUE, sigm = sigma(object),
use.hessian = NULL, ...)
## S3 method for class 'merMod'
model.frame(formula, fixed.only = FALSE, ...)
## S3 method for class 'merMod'
model.matrix(object, type = c("fixed", "random", "randomListRaw"), ...)
## S3 method for class 'merMod'
print(x, digits = max(3, getOption("digits") - 3),
correlation = NULL, symbolic.cor = FALSE,
signif.stars = getOption("show.signif.stars"), ranef.comp = "Std.Dev.", ...)
## S3 method for class 'merMod'
summary(object, correlation = , use.hessian = NULL, ...)
## S3 method for class 'summary.merMod'
print(x, digits = max(3, getOption("digits") - 3),
correlation = NULL, symbolic.cor = FALSE,
signif.stars = getOption("show.signif.stars"),
ranef.comp = c("Variance", "Std.Dev."), show.resids = TRUE, ...)
## S3 method for class 'merMod'
update(object, formula., ..., evaluate = TRUE)
## S3 method for class 'merMod'
weights(object, type = c("prior", "working"), ...)
Arguments
object
an R object of class merMod, i.e.,
as resulting from lmer(), or glmer(),
etc.
x
an R object of class merMod or summary.merMod,
respectively, the latter resulting from summary(<merMod>).
fit
an R object of class merMod.
formula
in the case of model.frame, a
merMod object.
refit
logical indicating if objects of class lmerMod should be
refitted with ML before comparing models. The default is
TRUE to prevent the common mistake of inappropriately
comparing REML-fitted models with different fixed effects,
whose likelihoods are not directly comparable.
model.names
character vectors of model names to be used in the
anova table.
scale
Not currently used (see extractAIC).
k
see extractAIC.
REML
Logical. If TRUE, return the restricted log-likelihood
rather than the log-likelihood. If NULL (the default),
set REML to isREML(object) (see isREML).
fixed.only
logical indicating if only the fixed effects
components (terms or formula elements) are sought. If false, all
components, including random ones, are returned.
random.only
complement of fixed.only; indicates
whether random components only are sought. (Trying to specify
fixed.only and random.only at the same time
will produce an error.)
correlation
(logical)
for vcov, indicates whether the correlation matrix as well as
the variance-covariance matrix is desired;
for summary.merMod, indicates whether the correlation matrix
should be computed and stored along with the covariance;
for print.summary.merMod, indicates whether the correlation
matrix of the fixed-effects parameters should be printed. In the
latter case, when NULL (the default), the correlation matrix
is printed when it has been computed by summary(.), and when
p <= 20.
use.hessian
(logical) indicates whether to use the
finite-difference Hessian of the deviance function to compute
standard errors of the fixed effects, rather estimating
based on internal information about the inverse of
the model matrix (see getME(.,"RX")).
The default is to to use the Hessian whenever the
fixed effect parameters are arguments to the deviance
function (i.e. for GLMMs with nAGQ>0), and to use
getME(.,"RX") whenever the fixed effect parameters are
profiled out (i.e. for GLMMs with nAGQ==0 or LMMs).
use.hessian=FALSE is backward-compatible with older versions
of lme4, but may give less accurate SE estimates when the
estimates of the fixed-effect (see getME(.,"beta"))
and random-effect (see getME(.,"theta")) parameters
are correlated.
sigm
the residual standard error; by default sigma(object).
digits
number of significant digits for printing
symbolic.cor
should a symbolic encoding of the fixed-effects correlation
matrix be printed? If so, the symnum function is used.
signif.stars
(logical) should significance stars be used?
ranef.comp
character vector of length one or two, indicating
if random-effects parameters should be reported on the variance and/or
standard deviation scale.
show.resids
should the quantiles of the scaled residuals be
printed?
formula.
see update.formula.
evaluate
see update.
type
For weights, type of weights to be returned; either "prior" for
the initially supplied weights or "working" for the weights
at the final iteration of the penalized iteratively reweighted least
squares algorithm. For model.matrix, type of model matrix to
return (one of fixed giving the fixed effects model matrix,
random giving the random effects model matrix, or
randomListRaw giving a list of the raw random effects model
matrices associated with each random effects term).
...
potentially further arguments passed from other methods.
Objects from the Class
Objects of class merMod are created by calls to
lmer, glmer or nlmer.
S3 methods
The following S3 methods with arguments given above exist (this list is currently not complete):
anova:
returns the sequential decomposition of the contributions of
fixed-effects terms or, for multiple arguments, model comparison statistics.
For objects of class lmerMod the default behavior is to refit the models
with LM if fitted with REML = TRUE, this can be controlled via the
refit argument. See also anova.
coef:
Computes the sum of the random and fixed effects
coefficients for each explanatory variable for each level of each
grouping factor.
extractAIC:
Computes the (generalized) Akaike An
Information Criterion. If isREML(fit), then fit is
refitted using maximum likelihood.
family:
family of fitted
GLMM. (Warning: this accessor may not work properly with
customized families/link functions.)
fitted:
Fitted values, given the conditional modes of
the random effects. For more flexible access to fitted values, use
predict.merMod.
logLik:
Log-likelihood at the fitted value of the
parameters. Note that for GLMMs, the returned value is only
proportional to the log probability density (or distribution) of the
response variable. See logLik.
model.frame:
returns the frame slot of merMod.
model.matrix:
returns the fixed effects model matrix.
nobs, ngrps:
Number of observations and vector of
the numbers of levels in each grouping factor. See ngrps.
summary:
Computes and returns a list of summary statistics of the
fitted model, the amount of output can be controlled via the print method,
see also summary.
print.summary:
Controls the output for the summary
method.
vcov:
Calculate variance-covariance matrix of the fixed
effect terms, see also vcov.
update:
See update.
Deviance and log-likelihood of GLMMs
One must be careful when defining the deviance of a GLM. For example,
should the deviance be defined as minus twice the log-likelihood or
does it involve subtracting the deviance for a saturated model? To
distinguish these two possibilities we refer to absolute deviance
(minus twice the log-likelihood) and relative deviance (relative to a
saturated model, e.g. Section 2.3.1 in McCullagh and Nelder 1989).
With GLMMs however, there is an additional complication involving the
distinction between the likelihood and the conditional likelihood.
The latter is the likelihood obtained by conditioning on the estimates
of the conditional modes of the spherical random effects coefficients,
whereas the likelihood itself (i.e. the unconditional likelihood)
involves integrating out these coefficients. The following table
summarizes how to extract the various types of deviance for a
glmerMod object:
conditional
unconditional
relative
deviance(object)
NA in lme4
absolute
object@resp$aic()
-2*logLik(object)
This table requires two caveats:
If the link function involves a scale parameter
(e.g. Gamma) then object@resp$aic() - 2 * getME(object,
"devcomp")$dims["useSc"] is required for the absolute-conditional
case.
If adaptive Gauss-Hermite quadrature is used, then
logLik(object) is currently only proportional to the
absolute-unconditional log-likelihood.
For more information about this topic see the misc/logLikGLMM
directory in the package source.
Slots
resp:
A reference class object for an lme4
response module (lmResp-class).
Gp:
See getME.
call:
The matched call.
frame:
The model frame containing all of the variables
required to parse the model formula.
flist:
See getME.
cnms:
See getME.
lower:
See getME.
theta:
Covariance parameter vector.
beta:
Fixed effects coefficients.
u:
Conditional model of spherical random effects
coefficients.
devcomp:
See getME.
pp:
A reference class object for an lme4
predictor module (merPredD-class).
optinfo:
List containing information about the
nonlinear optimization.